Date: Thu, 22 Jun 2000 17:39:03 +0200 (MET DST)
From: Arun-Kumar Tripathi <tripathi-AT-statistik.uni-dortmund.de>
Subject: EUCLID [334? - 280 B.C.]    


Greetings technology lists,

I have re-written my own article on great Euclid, which was earlier
published in the Science Master Magazine in India way back in 1983. What
do you think of this? Please let me know. Thanks --Arun 
--

                           EUCLID: A GREAT MATHMATECIAN
                         ---------------------------------

 WHO has not heard of Euclid during his first lessons in geometry in
the school. He gave the geometry of the universe on which Newton built his
laws of gravitation and motion. It was only in the 19th century that the
Limitation of Euclid's geometry as applied to space was first discovered
by Nicholas Lobatchevsky and later by Einstein who completely repudiated
the Euclidean geometry in his Relativity Theory. However, Euclidean
geometry and the Newtonian laws are the one which are most valid on earth.

Early Days:-
-----------

 Euclid seemed to have studied in Plato's Academy, the then best known
School of Mathematics - a Cambridge of Greece. He was believed to be a
Phoenician with a greek outlook. It was the period when Alexander Of
Macedonia, after his world conquest, had established the township of
Alexandria in Egypt. Ptolemy, the governor of Alexandria in Egypt, Ptolemy
was a learned amn and he founded the great university of Alexandria which
surpassed even Plato's Academy. There Euclid was invited to teach
geometry.

A great Experimenter:-
-----------------------

 He learned more through applications like constructions of pumps,
fountains, and steam drive motors. Euclid achieved things which were the
thought impossible. His fellow professors thought it is impossible to
measure the height of the great pyramid. But Euclid waited near the
pyramid measuring his own shadow. At the hour when it became equal to his
own height, he quickly measured the length of the shadow cast by the
pyramid and offered it as the height of the same. This was one of the
consequences of his study of the propagation of light in staright lines,
the other being his discovery of the laws of formation of images by
mirrors.

The Great Geometrician:-
------------------------

  Euclid raised geometry to the highest level and he published 13 books
called 'Elements' which caontained  the basic principles, the statements
and proofs of theorems. Even after two and half millennia these books
remain the standard texts in geometry, and wherever geometry is taught,
there resides Euclid.

Euclid and Infinity:-
---------------------

  Euclid tried to solve the three classical problems of trisecting and
angle, doubling a cube and squaring a circle. The First problem has a
cubic equation 4x3-3x-a=0, where 'a' is a given number. The problem of
doubling the cube  also rsolved into a cubic equation(2x3=y3).

  Greeks of Euclid's time were not equipped with graduated instruments
which alone could solve a cubic equation. The story is that once the
Delphian Oracle predicted a military victory, provided the Athenians would
double the siege of the Altar of Apollo. The Expedition was lost because
instead of doubling the siege, they doubled the length. breadth and height
of the Altar which meant an Eight Fold Enlargement.

The Third Problem of squaring the circle involves the finding of the Exact
value of Pi, the ratio between a circle and its diameter, the Pi belongs
to the irrational number or unspeakable number of Pythagoras and Euclid
proved that it was a wastage of time to expect an exact value of Pi,
because his solutions ended up in absurd contradictions showing that no
exact ratio existed between the entities sought.

However, his work with the primes and the irrational numbes dissuaded him
from the investigation of INFINITY and today even after 2500 years no one
can exactly define the role of Infinity of Mathematics   
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